\subsubsection*{Evaluation by Simulation}
To evaluate the analytical expression for the decoding probability, found in Equation \eqref{eq:nw_l1_anal} for \ac{L1} and Equation \eqref{eq:nw_l2_anal} for \ac{L1} and \ac{L2}, a simulation of \ac{UEP} by \ac{NW} has been designed. The evaluation is based on the $\boldsymbol \Gamma$ distributions in Figure \ref{fig:new_decoding_plots} which is considered a good representation of the range of $\boldsymbol \Gamma$. To verify the correctness of the analytical expression the difference between the analytical and simulated probabilities is given in Figure \ref{fig:diff_plot_new_l1} and \ref{fig:diff_plot_new_l2}. The source code and data output for the simulation is available on the Project DVD \cite{cd}.

%\begin{figure} \centering
%\subfloat[]{\label{}\includegraphics}\\
%\subfloat[]{\label{}\includegraphics[width=1\textwidth]{}}\\
%\caption{The difference between the simulated and analytical decoding probabilities for the two-layered NW UEP method, given in percentage points ([pp]).}
%\label{fig:diff_plot_new}
%\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{figs/l1_new_dif.eps}
\caption{Difference between the simulated and analytical decoding probabilities for L1 using NW UEP, given in percentage points ([pp]).}
\label{fig:diff_plot_new_l1}
\end{figure}


\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{figs/l2_new_dif.eps}
\caption{Difference between the simulated and analytical decoding probabilities for L2 using NW UEP, given in percentage points ([pp]).}
\label{fig:diff_plot_new_l2}
\end{figure}

\newpage

The simulated and analytical probabilities shows a small difference. The peak deviation is $\approx 1.3$ percentage point on \ac{L1} with $\boldsymbol \Gamma_1=0.4$ as seen in Figure \ref{fig:diff_plot_new_l1}. The deviation is not considered critical because the difference in general seem of fairly random nature. A theory for the source of the divergence is the simulations implementation af a random-function to generate \ac{RLNC} vectors. The random-function is pseudo-random and will converge to uniformity. The simulation is run a finite number of iterations which can generate a slight bias in the vector generation. The presented results is considered to prove the validity of the analytical expression for \ac{NC} with \ac{UEP} by \ac{NW}, thereby allowing further use of the analytical expressions.
